03482nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205072001600228100008300244245014600327250001800473264007300491300006300564336002600627337002600653338003600679347002400715490006600739505064600805520101401451650002102465650002102486700008702507700008502594710003402679773002602713776003602739776003602775776003602811830007302847856004602920912001402966912001502980999001702995978-3-031-73430-4DE-He21320251030114610.0cr nn 008mamaa241210s2024    sz |    s    |||| 0|eng d  a97830317343049978-3-031-73430-47 a10.1007/978-3-031-73430-42doi 4aQA329-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh 7aPBKF2thema1 aAlpay, Daniel.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97655610aQuaternionic Hilbert Spaces and Slice Hyperholomorphic Functionsh[electronic resource] /cby Daniel Alpay, Fabrizio Colombo, Irene Sabadini.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXI, 348 p. 29 illus., 1 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aOperator Theory: Advances and Applications,x2296-4878 ;v3040 a- Part I Quaternionic functional analysis and related topics -- Functions of a Quaternionic Variable -- Quaternionic Banach and Hilbert Spaces -- Quaternionic Linear Operators on a Hilbert Space -- Reproducing Kernel Hilbert Spaces -- Part II Spaces of Slice Hyperholomorphic Functions -- Slice Hyperholomorphic Hardy Spaces -- de Branges Spaces -- Slice Hyperholomorphic Bergman Spaces -- Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces -- Slice Hyperholomorphic Fock Space -- Wiener Algebras -- Part III Various Extensions -- Slice Polyanalytic Functions -- Several Quaternionic Variables -- Function Spaces and Spectral Theories.  aThe purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented. 0aOperator theory.14aOperator Theory.1 aColombo, Fabrizio.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9291371 aSabadini, Irene.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9291382 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303173429808iPrinted edition:z978303173431108iPrinted edition:z9783031734328 0aOperator Theory: Advances and Applications,x2296-4878 ;v30497461740uhttps://doi.org/10.1007/978-3-031-73430-4  aZDB-2-SMA  aZDB-2-SXMS  c65601d65601